integral from 0 to 2 of 12x^3sqrt(9+x^4)

Lösung

\int_{0}^{2} 12 x^{3} 9 + x^{4} d x

196

Schritte zur Lösung

\int_{0}^{2} 12 x^{3} 9 + x^{4} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 12 \cdot \int_{0}^{2} x^{3} 9 + x^{4} d x

Wende U-Substitution an

= 12 \cdot \int_{9}^{25} \frac{u}{4} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 12 \cdot \frac{1}{4} \cdot \int_{9}^{25} u d u

Wende die Potenzregel an

= 12 \cdot \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{9}^{25}

Vereinfache

12 \cdot \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{9}^{25} : 3 [\frac{2}{3} u^{\frac{3}{2}}]_{9}^{25}

= 3 [\frac{2}{3} u^{\frac{3}{2}}]_{9}^{25}

Berechne die Grenzen:

\frac{196}{3}

= 3 \cdot \frac{196}{3}

Vereinfache

= 196

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